Recursive Least-squares Estimation Research Articles

An unwindowed multichannel lattice filter with orthogonal channels

An unwindowed (or covariance) multichannel lattice filter for recursive least-squares estimation is derived. The channels are orthogonalized to eliminate the need for matrix inversion. The channel-orthogonalization process leads to forward-propagating and backward-propagating blocks in both the lattice filter and the model-parameter construction algorithm. These blocks are particularly suitable for array processing, as illustrated by arrays presented in the paper.

Adaptive control: state of the art and an application to a grinding process

Adaptive control is finding its way into real-life situations, mainly as a result of considerable advances in microelectronics and the understanding of adaptive control theory. Several adaptive control algorithms are now available and many industrial applications have been performed in the field of chemical engineering and more recently in the field of particulate processes. This paper gives an overview of discrete adaptive controllers. It presents qualitatively the underlying control design and discusses the recursive least-squares estimation algorithm with requirements for long-term parameter tracking. Particular emphasis is put on the design assumptions and several adaptive control applications in the particulate process field are given. Results concerning the adaptive control of a simulated grinding circuit are detailed.

Generalized predictive control (GPC) with long-range predictive identification (LRPI) for multivariable anaesthesia

Early and current self-tuning algorithm formulations were generally based on the assumption that the process model under investigation is linear within a certain operating point. A standard Recursive Least-Squares (RLS) estimation algorithm was used to update the model parameters whose data input and output were normally fed through a filter with adequate characteristics. One of the most popular themes belonging to this class of adaptive controllers is that of generalized predictive control (GPC). Classified in the category of long-range predictive controllers (LRPC) its control law stems from the minimization of a cost function over a horizon which spans that used by the RLS algorithm (one step ahead). This paper describes a new approach which derives the same model parameters using extra filtering provided by an identification objective similar to the one used for control derivation. Already successfully applied in real-time to a SISO control system by its original authors, the scheme, known as long-ran...

A class of robust image processors

In this paper robust recursive estimators for image restoration are developed. Image restoration for images corrupted by noise is carried out in two steps. To preserve true edges while restoring, edge detection using a 5 × 5 × 5 × 5 Graeco-Latin square is carried out as a first step. An edge is localized using an F-test on contrasts. The center pixel is then estimated as a second step. The method of estimation of a center pixel uses a multiple linear regression model fitted to the noisy image part on the same side of the edge. Parameters of a multiple linear regression model are estimated recursively using the Robbins-Monro Stochastic Approximation procedure applied to the least-squares estimator. When noise departs from a Gaussian assumption, robust techniques for restoration are sought. The recursive least-squares estimator is robustized using Huber's maximum likelihood estimator of location parameter of the - f′/ f type, where - f′/ f is approximated by an M-interval polynomial approximation algorithm, and f is the p.d.f. of noise. A minimax estimator based on a soft limiter is used to robustize the recursive least-squares estimator as a computationally simpler but slightly less efficient alternative. The theory developed in this paper was tested using computer simulations which verified the theory and evaluated the computational complexity/simplicity of the methods.

Influence of the Initial Covariance Matrix on Recursive LS Estimation of Continuous Models via Generalised Poisson Moment Functionals

This paper presents the results of an investigation on the quality of recursive parameter estimation via the ordinary and normalised Poisson moment functional approach. It is shown that the ordinary and the normalised approach have different requirements for the initial value of the covariance matrix in the recursive least-squares estimation algorithm. Correctly initialised, both approaches supply the same results, letting aside numerical problems.

Recursive least-squares algorithms of modified Gram-Schmidt type for parallel weight extraction

This paper presents some new algorithms for parallel weight extraction in the recursive least-squares (RLS) estimation based on the modified Gram-Schmidt (MGS) method. These are the counterparts of the algorithms using an inverse QR decomposition based on the Givens rotations and do not contain the square root operation. Systolic-array implementations of the algorithms are considered on a 2-D rhombic array. Simulation results are also presented to compare the finite word-length effect of these new algorithms and existing algorithms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On‐line parameter interval estimation using recursive least squares

AbstractA bank of recursive least‐squares (RLS) estimators is proposed for the estimation of the uncertainty intervals of the parameters of an equation error model (or RLS model) where the equation error is assumed to lie between known upper and lower bounds. It is shown that the off‐line least‐squares method gives the maximum and minimum parameter values that could have produced the recorded input‐output sequence. By modifying the RLS estimator in two ways, it is possible to recursively compute inner and outer bounds of the uncertainty intergals. It is shown that the inner bound is asymptotically tight.

Adaptive control of flexible multilink manipulators

An adaptive self-tuning control scheme is developed for end-point position control of flexible manipulators. The proposed scheme has three characteristics. First, it is based on a dynamic model of a flexible manipulator described in cartesian coordinates, which eliminates the burden and inaccuracy of translating a desired end-point trajectory to joint coordinates using inverse kinematic relations. Second, the effect of flexibility is included in the dynamic model by approximating flexible links with a number of rigid sublinks connected at fictitious joints. The relatively high stiffness of the fictitious joints is shown to result in a decomposition of the model into two subsystems operating at different rates. This allows for stabilization of the oscillatory modes associated with the flexible links by a fast feedback control in addition to a slower control for trajectory tracking. Third, the control is constructed from measurements of the end-point position and deformations of the flexible links, with the manipulator parameters required to form the control obtained using a recursive least-squares estimation algorithm, which is fast enough for on-line applications. Satisfactory results are obtained from digital simulation of a two-link flexible manipulator.

Design of an Adaptive Model Matching Controller for Nonminimum Phase Systems Using a Periodic Scheme

Using a periodic control scheme, a direct adaptive model matching controller is proposed for a discrete-time multivariable nonminimum-phase system. The linear error equation for estimating appropriate periodic feedback gains and, at the same time, appropriate pole-placing feedback gains is first obtained using a derivation of the inverse system representation. With these periodic feedback gains estimated through the recursive leastsquare estimation scheme and used in a direct adaptive control law, it is then shown that the overall control system is globally asymptotically stable and the desired model matching is asymptotically achieved.

Joint signal detection and parameter estimation in multiuser communications

The problem of simultaneously detecting the information bits and estimating signal amplitudes and phases in a K-user asynchronous direct-sequence spread-spectrum multiple-access communication system is addressed. The joint maximum-likelihood (ML) estimator has a computational complexity that is exponential in the total number of bits transmitted and thus does not represent a practical solution to the problem. An estimator that combines a suboptimum tree-search algorithm with a recursive least-squares estimator of complex signal amplitude is considered. The complexity of this estimator is O(K/sup 2/) computations per decoded bit, and its performance is very close to that of the joint ML receiver. This receiver has the advantage that the transmitted signal powers and phases are extracted from the received signal in an adaptive fashion without using a test sequence.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Estimation of parameter errors from measurement residuals in state estimation (power systems)

Any error of network parameters affects the value of the measurement residuals calculated in state estimation. Explicit mathematical expressions relating the residuals to the parameter errors are derived. A two-step approach is proposed for parameter error estimation. The first step is to estimate a bias vector which combines the effects of parameter errors and the state of the system. A least-square approach using the measurement residuals calculated in each state estimation run is proposed for the first step. After several state estimation runs, a sequence of such bias vectors is obtained. The second step is to estimate the parameter errors from the sequence of bias vectors. A recursive least-square estimation method is proposed for this step. Theoretical and computational issues of the proposed method are addressed. Test results are presented. >

Identification of synchronous machine parameters from standstill tests using recursive estimation with the bilinear operator

A new method, based on standstill tests, is proposed for identifying the direct- and quadrature-axis parameters for a model of a synchronous machine. The method employs a recursive least-squares estimator to identify a discrete-time bilinear-operator model which closely approximates the continuous-time Laplace-operator model of a system. Some advantages of this method over conventional steady-state standstill frequency-response tests are flexibility of the type of input excitation used, the short time required to run the test, and that the models are obtained directly in parametric form. The method is demonstrated on a 5 kVA synchronous machine.

Lattice filters for RLS estimation of a delta operator-based model

A lattice filter algorithm is derived for the recursive least-squares (RLS) estimation of the parameters of the input-output model of a plant, based on the delta-operator formulation. The lattice derivation presented allows a numerically efficient implementation, particularly for large orders. The order-recursive property of the lattices is ideally suited for order determination techniques and applications where the order of the plant may change during operation. An example concerning parameter identification for a fourth-order plant with measurement noise is given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A least-squares based model-fitting identification technique for diesel prime-movers with unknown dead-time

The recursive least-squares estimation technique is extended for application to systems with small but unknown dead-time delays. This problem is studied with particular reference to when the diesel engine is used as a prime-mover, in which case the dead-time leads to a significant variation in dynamic performance. In practice, least-squares estimators are found to have slow convergence and large output errors, when applied to systems with time-delays. It is shown that by a suitably constrained algorithm, convergence can be quickened and output error can be kept within acceptable limits. Low-order system models with changing dead-time are in general, characterized by modeling errors that are to an extent correlated with the input control signal to the plant. Despite this fact, the developed approach yields very small prediction errors, even when large deterministic disturbances are present. This suggests its possible use in conjunction with adaptive controllers of various types. >

On-Line Least-Squares Method of Estimating the Coefficients of the Orthogonal-Polynomial Expansion of a Function

A recursive least-square estimation algorithm has been developed for finding the coefficients of the Laguerre- polynomial expansion of a signal, when a finite set of polynomials are used to represent the signal. We have shown how the same algorithm can be used for both the single and double variable functions. Numerical results are given to illustrate the algorithm.

ITERATIVE AND RECURSIVE ESTIMATION OF TRANSFER FUNCTIONS

Abstract. A unified treatment of non‐linear estimation, pseudolinear regression and stochastic approximation for open‐loop transfer function models is provided. Pseudolinear regression techniques are used to derive the recursive non‐linear least‐squares estimator, avoiding the methodological problems implicit in traditional derivations. Stochastic approximation analysis is used to investigate in a direct manner the conditions of convergence and consistency of both iterative and recursive algorithms. The various methods are compared using data for an industrial process.

Nondefinite least squares and its relation to H/sub infinity /-minimum error state estimation

The problem of recursive nondefinite least-squares state estimation of continuous-time stationary processes is solved, by applying Pontryagin's maximum principle. A comparison of the derived solution to the result that is obtained for the H/sub infinity /-minimum error estimation suggests a new interpretation for the H/sub infinity /-optimal estimation mechanism. According to this interpretation, the estimator tries to optimally estimate the required combination of the states, in the l/sub 2/-norm sense, against the worst disturbance signal that stems from a fictitious measurement of this combination.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Self-tuning control of non-linear ARMAX models

A control-weighted self-tuning minimum-variance controller with a non-linear difference equation structure is described. An extended recursive least-squares estimation algorithm is employed to provide the adaptiveness. Performance analysis of the controller is discussed in terms of a cumulative loss function and high-order correlation functions of the system input, output and residual sequences. Simulation results from an experiment using a model identified from a real system are also provided.

Stability control of multimachine power systems using STAC technique

A new control strategy is proposed for implementing stability controls of interconnected multimachine power systems. This new strategy is of a decentralized nature and is implemented locally by using a self-tuning adaptive controller (STAC). The STAC is composed of the recursive least-squares (RLS) estimation algorithm with variable-forgetting-factor incorporated with the generalized minimum-variance control technique. A discrete input/output model is developed to represent each subsystem of the system under consideration. A computer simulation is performed on a 4-machine system to test the validity and effectiveness of the proposed control strategy.

Sliding-windowed weighted recursive least-squares method for parameter estimation

This letter presents a modified method of the exponentially weighted recursive least-squares (WRLS) estimation using sliding window. In the method, two windowing techniques are simultaneously used to ensure that the estimator has good parameter tracking property and that the estimated parameters converge the true parameters. Simulation shows that the proposed method tracks rapidly time-varying parameters more effectively than WRLS.